Description

This book is designed for teachers of children in grades 3 to 7. It shows how Vedic Mathematics can be used in a school course but does not cover all school topics (see contents). The book can be used for teachers who wish to learn the Vedic system or to teach courses on Vedic mathematics for this level.

The Manual contains many topics that are not in the other Manuals that are suitable for this age range and many topics that are also in Manual 2 are covered in greater detail here.

Details

Please note that these Manuals do not form a sequence: there is some overlap between the three books.

Reviews

"The author should be commended for his thorough grasp of Krishna Tirthaji's book on Vedic Mathematics, his layout of the divisions of mathematics and various exercises provided for the students which enhance the value of these books [Teacher's Manuals]. They are ideal companions for the teacher and adult students alike."- Journal of oriental research, Vol. 78-80, 2006-9.

"I am a student of class XI and planning to appear in IIT entrance exam next year and would like to take this opportunity of telling you what a difference your books have made to my life. I hated maths till class x and believed that it is the only subject which was a brain freak and I felt that I could never achieve excellent marks in math’s, as I could in other subjects. I am extremely thankful to you for writing these books. They are great source of encouragement for me and many other students like me. I have read your primary level and dying to read next two levels..."Rajesh Gupta

Preface

PREFACE

This Manual is the first of three (elementary, intermediate and advanced) Manuals which are designed for adults with a basic understanding of mathematics to learn or teach the Vedic system. So teachers could use it to learn Vedic Mathematics, though it is not suitable as a text for children (for that the Cosmic Calculator Course is recommended). Or it could be used to teach a course on Vedic Mathematics.

The sixteen lessons of this course are based on a series of one week summer courses given at Oxford University by the author to Swedish mathematics teachers between 1990 and 1995. Those courses were quite intensive consisting of eighteen, one and a half hour, lessons.

All techniques are fully explained and proofs are given where appropriate, the relevant Sutras are indicated throughout (these are listed at the end of this Manual) and, for convenience, answers are given after each exercise. Cross-references are given showing what alternative topics may be continued with at certain points.

It should also be noted that the Vedic system encourages mental work so we always encourage students to work mentally as long as it is comfortable. In the Cosmic Calculator Course pupils are given a short mental test at the start of most or all lessons, which makes a good start to the lesson, revises previous work and introduces some of the ideas needed in the current lesson. In the Cosmic Calculator course there are also many games that help to establish and promote confidence in the ideas used here.

Some topics will be found to be missing in this text: for example, there is no section on area, only a brief mention. This is because the actual methods are the same as currently taught so that the only difference would be to give the relevant Sutra(s).

Introduction

INTRODUCTION

Vedic Mathematics is an ancient system of mathematics which was rediscovered early last century by Sri Bharati Krsna Tirthaji (henceforth referred to as Bharati Krsna).

The Sanskrit word “veda” means “knowledge”. The Vedas are ancient writings whose date is disputed but which date from at least several centuries BC. According to Indian tradition the content of the Vedas was known long before writing was invented and was freely available to everyone. It was passed on by word of mouth. The writings called the Vedas consist of a huge number of documents (there are said to be millions of such documents in India, many of which have not yet been translated) and these have recently been shown to be highly structured, both within themselves and in relation to each other (see Reference 2). Subjects covered in the Vedas include Grammar, Astronomy, Architecture, Psychology, Philosophy, Archery etc., etc.

A hundred years ago Sanskrit scholars were translating the Vedic documents and were surprised at the depth and breadth of knowledge contained in them. But some documents headed “Ganita Sutras”, which means mathematics, could not be interpreted by them in terms of mathematics. One verse, for example, said “in the reign of King Kamse famine, pestilence and unsanitary conditions prevailed”. This is not mathematics they said, but nonsense.

Bharati Krsna was born in 1884 and died in 1960. He was a brilliant student, obtaining the highest honours in all the subjects he studied, including Sanskrit, Philosophy, English, Mathematics, History and Science. When he heard what the European scholars were saying about the parts of the Vedas which were supposed to contain mathematics he resolved to study the documents and find their meaning. Between 1911 and 1918 he was able to reconstruct the ancient system of mathematics which we now call Vedic Mathematics.

He wrote sixteen books expounding this system, but unfortunately these have been lost and when the loss was confirmed in 1958 Bharati Krsna wrote a single introductory book entitled “Vedic Mathematics”. This is currently available and is a best-seller (see Reference 1).

There are many special aspects and features of Vedic Mathematics which are better discussed as we go along rather than now because you will need to see the system in action to appreciate it fully. But the main points for now are:

1) The system rediscovered by Bharati Krsna is based on sixteen formulae (or Sutras) and some sub-formulae (sub-Sutras). These Sutras are given in word form: for example By One More than the One Before and Vertically and Crosswise. In this text they are indicated by italics. These Sutras can be related to natural mental functions such as completing a whole, noticing analogies, generalisation and so on.

2) Not only does the system give many striking general and special methods, previously unknown to modern mathematics, but it is far more coherent and integrated as a system.

3) Vedic Mathematics is a system of mental mathematics (though it can also be written down).

Many of the Vedic methods are new, simple and striking. They are also beautifully interrelated so that division, for example, can be seen as an easy reversal of the simple multiplication method (similarly with squaring and square roots). This is in complete contrast to the modern system. Because the Vedic methods are so different to the conventional methods, and also to gain familiarity with the Vedic system, it is best to practice the techniques as you go along.

THE FIRST BY THE FIRST AND THE LAST BY THE LAST THE FIRST BY THE FIRST THE LAST BY THE LAST

DIVISIBILITY BY 4

DIVISIBILITY BY 11 REMAINDER AFTER DIVISION BY 11 ANOTHER DIGIT SUM CHECK

LESSON 9 BAR NUMBERS

REMOVING BAR NUMBERS ALL FROM 9 AND THE LAST FROM 10

SUBTRACTION

CREATING BAR NUMBERS

USING BAR NUMBERS

LESSON 10 SPECIAL MULTIPLICATION

MULTIPLICATION BY 11 CARRIES LONGER NUMBERS

BY ONE MORE THAN THE ONE BEFORE

MULTIPLICATION BY NINES

THE FIRST BY THE FIRST AND THE LAST BY THE LAST

USING THE AVERAGE

SPECIAL NUMBERS REPEATING NUMBERS PROPORTIONATELY DISGUISES

LESSON 11 GENERAL MULTIPLICATION

REVISION

TWO-FIGURE NUMBERS CARRIES

MOVING MULTIPLIER

EXTENSION

MULTIPLYING BINOMIALS

MULTIPLYING 3-FIGURE NUMBERS

WRITTEN CALCULATIONS

LESSON 12 SQUARING

SQUARING NUMBERS THAT END IN 5

SQUARING NUMBERS NEAR 50

GENERAL SQUARING THE DUPLEX

NUMBER SPLITTING

ALGEBRAIC SQUARING

DIGIT SUMS OF SQUARES

SQUARE ROOTS OF PERFECT SQUARES

3 AND 4 FIGURE NUMBERS

LESSON 13 EQUATIONS

ONE-STEP EQUATIONS

TWO-STEP EQUATIONS

THREE-STEP EQUATIONS

LESSON 14 FRACTIONS

VERTICALLY AND CROSSWISE

A SIMPLIFICATION

COMPARING FRACTIONS

UNIFICATION OF OPERATIONS

LESSON 15 SPECIAL DIVISION

DIVISION BY 9 LONGER NUMBERS CARRIES A SHORT CUT

DIVISION BY 8 ETC.

DIVISION BY 99, 98 ETC.

DIVISOR BELOW A BASE NUMBER TWO-FIGURE ANSWERS

DIVISOR ABOVE A BASE NUMBER

LESSON 16 THE CROWNING GEM

SINGLE FIGURE ON THE FLAG

SHORT DIVISION DIGRESSION

LONGER NUMBERS

NEGATIVE FLAG DIGITS

DECIMALISING THE REMAINDER

SUTRAS AND SUB-SUTRAS

9-POINT CIRCLES

REFERENCES

INDEX OF THE VEDIC FORMULAE

INDEX

Back Cover

VEDIC MATHEMATICS MANUAL

ELEMENTARY LEVEL

¯ Vedic Mathematics was reconstructed from ancient Vedic texts early last century by Sri Bharati Krsna Tirthaji (1884-1960). It is a complete system of mathematics which has many surprising properties and applies at all levels and areas of mathematics, pure and applied.

¯ It has a remarkable coherence and simplicity that make it easy to do and easy to understand. Through its amazingly easy methods complex problems can often be solved in one line.

¯ The system is based on sixteen word-formulae (Sutras) that relate to the way in which we use our mind.

¯ The benefits of using Vedic Mathematics include more enjoyment of maths, increased flexibility, creativity and confidence, improved memory, greater mental agility and so on.

¯ This Elementary Manual is the first of three designed for teachers who wish to teach the Vedic system, either to a class or to other adults/teachers. It is also suitable for anyone who would like to teach themselves the basic Vedic methods.